Q 11-07-014JEE MainAIEEE 2011Medium
Two bodies of masses $m$ and $4m$ are placed at a distance $r$. The gravitational potential at a point on the line joining them where the gravitational field is zero is
Answer: (A) $-\dfrac{9Gm}{r}$
Concept. First find the neutral point, where the two fields cancel. Then add the potentials there. Potential is a scalar, and both contributions are negative, so they add up; they do not cancel.
Step 1. Neutral point. Let it be at $x$ from $m$:
$$\frac{Gm}{x^2}=\frac{G(4m)}{(r-x)^2}\ \Rightarrow\ r-x=2x\ \Rightarrow\ x=\frac r3$$
Step 2. Potential there.
$$V=-\frac{Gm}{r/3}-\frac{G(4m)}{2r/3}=-\frac{3Gm}{r}-\frac{6Gm}{r}=-\frac{9Gm}{r}$$
Answer. Option A. Zero field does not mean zero potential.
Solution by Sreeraj P, M.Sc Physics
